Skip to Main Content
Coursera

Press the up and down arrow key to navigate

    Goals
  • Take a free course
    Subjects
  • Browse all subjects

Earn a Degree

Breakthrough pricing on 100% online degrees designed to fit into your life.

Data Science

University of Colorado Boulder Logo
University of Colorado Boulder
Master of Science in Data Science
University of Illinois at Urbana-Champaign Logo
University of Illinois at Urbana-Champaign
Master in Computer Science
View all Data Science degrees

Business

University of Illinois at Urbana-Champaign Logo
University of Illinois at Urbana-Champaign
Master of Business Administration (iMBA)
University of Illinois at Urbana-Champaign Logo
University of Illinois at Urbana-Champaign
Master of Science in Management
View all Business degrees

Computer Science

Penn Engineering Logo
Penn Engineering
Master of Computer and Information Technology
Arizona State University Logo
Arizona State University
Master of Computer Science
View all Computer Science degrees

More Degrees

Public HealthBachelor's DegreesEngineeringMaster's DegreesSocial Sciences

Earn credit toward a master's

undefined Logo
Big Data MasterTrack® Certificate
Degree credit•Expert feedback
undefined Logo
Innovation Management & Entrepreneurship MasterTrack® Certificate
Degree credit•Expert feedback
View all MasterTrack Certificates

Earn a Certificate

In 3-9 months, gain the skills to break into a new career or take your career to the next level.

Data Science

undefined Logo
Google Data Analytics
No prerequisites•Self-paced
undefined Logo
IBM Data Science
No prerequisites•Self-paced
undefined Logo
Machine Learning for Analytics MasterTrack® Certificate
Expert feedback•Credit eligible
View all Data Science Certificates

Business

undefined Logo
Facebook Social Media Marketing
No prerequisites•Self-paced
undefined Logo
Google Project Management:
No prerequisites•Self-paced
undefined Logo
IBM Machine Learning
Self-paced
View all Business Certificates

Computer Science

undefined Logo
AI and Machine Learning MasterTrack® Certificate
Expert feedback•Credit eligible
undefined Logo
DeepLearning.AI TensorFlow Developer
Certification preparation•Self-paced
undefined Logo
Software Engineering MasterTrack® Certificate
Expert feedback•Credit eligible
View all Computer Science Certificates

More Certificate Programs

Computer SciencePhysical Science and EngineeringSocial SciencesLanguage Learning

Launch or advance your career

Data Science

Data ScientistData AnalystBI AnalystBI DeveloperData Engineer

Business

Agile Project Manager (IT)Digital Marketing SpecialistDigital Marketing ManagerProject CoordinatorProject ManagerSocial Media Coordinator

Computer Science

Computer User Support SpecialistNetwork AdministratorNetwork EngineerProduct Designer

Arts and Humanities

Graphic DesignerUI/UX DesignerView all Professional Certificates

Data Science

Get started

Free coursesMost popularGuided Projects under 2 hours

Popular skills

PythonSQLMicrosoft ExcelExcelMachine LearningData SciencePower BIArtificial IntelligenceStatisticsFree Courses Data ScienceView all skills

Degrees

Breakthrough pricing on 100% online degrees designed to fit into your life.
University of Colorado Boulder Logo
University of Colorado Boulder
Master of Science in Data Science
University of Illinois at Urbana-Champaign Logo
University of Illinois at Urbana-Champaign
Master in Computer Science
HSE University Logo
HSE University
Master of Data Science
View all degrees

Certificate programs

In 3-9 months, gain the skills to break into a new career or take your career to the next level.
undefined Logo
Google Data Analytics
No prerequisites•Self-paced
undefined Logo
IBM Data Science
No prerequisites•Self-paced
undefined Logo
Machine Learning for Analytics MasterTrack® Certificate
Expert feedback•Credit eligible
View all Certificates

Business

Get started

Free coursesMost popularGuided Projects under 2 hours

Popular skills

Project ManagementMicrosoft ExcelExcelBlockchainDigital MarketingStock MarketPower BIMarketingAccountingFree Courses Data ScienceView all skills

Degrees

Breakthrough pricing on 100% online degrees designed to fit into your life.
University of Illinois at Urbana-Champaign Logo
University of Illinois at Urbana-Champaign
Master of Business Administration (iMBA)
University of Illinois at Urbana-Champaign Logo
University of Illinois at Urbana-Champaign
Master of Science in Management
Macquarie University Logo
Macquarie University
Global Master of Business Administration (Global MBA)
View all degrees

Certificate programs

In 3-9 months, gain the skills to break into a new career or take your career to the next level.
undefined Logo
Facebook Social Media Marketing
No prerequisites•Self-paced
undefined Logo
Google Project Management:
No prerequisites•Self-paced
undefined Logo
IBM Machine Learning
Self-paced
View all Certificates

Computer Science

Get started

Free coursesMost popularGuided Projects under 2 hours

Popular skills

PythonJavaCybersecurityBlockchainWeb DevelopmentC++AWSArtificial IntelligenceJavascriptGuided ProjectsView all skills

Degrees

Breakthrough pricing on 100% online degrees designed to fit into your life.
Penn Engineering Logo
Penn Engineering
Master of Computer and Information Technology
Arizona State University Logo
Arizona State University
Master of Computer Science
HSE University Logo
HSE University
Master of Computer Vision
View all degrees

Certificate programs

In 3-9 months, gain the skills to break into a new career or take your career to the next level.
undefined Logo
AI and Machine Learning MasterTrack® Certificate
Expert feedback•Credit eligible
undefined Logo
DeepLearning.AI TensorFlow Developer
Certification preparation•Self-paced
undefined Logo
Software Engineering MasterTrack® Certificate
Expert feedback•Credit eligible
View all Certificates

Information Technology

Get started

Free coursesMost popularGuided Projects under 2 hours

Popular skills

GoogleCybersecurityAWSLinuxDevOpsEthical HackingMicrosoftAzureGoogle CloudKubernetesView all skills

Degrees

Breakthrough pricing on 100% online degrees designed to fit into your life.
Penn Engineering Logo
Penn Engineering
Master of Computer and Information Technology
Arizona State University Logo
Arizona State University
Master of Computer Science
University of Illinois at Urbana-Champaign Logo
University of Illinois at Urbana-Champaign
Master of Computer Science
View all degrees

Certificate programs

In 3-9 months, gain the skills to break into a new career or take your career to the next level.
undefined Logo
Google IT Support
No prerequisites•Self-paced
undefined Logo
Preparing for Google Cloud Certification: Cloud Architect
Certification preparation•Self-paced
undefined Logo
Cybersecurity MasterTrack® Certificate
Expert feedback•Credit eligible
View all Certificates

Language Learning

Get started

Free coursesMost popularGuided Projects under 2 hours

Popular skills

EnglishKoreanFrench LanguageEnglish SpeakingFrenchJapaneseChineseEnglish GrammarEnglish WritingKorean LanguageView all skills

Degrees

Breakthrough pricing on 100% online degrees designed to fit into your life.
National Research Tomsk State University Logo
National Research Tomsk State University
Global MA in English Language Teaching Leadership
View all degrees

Certificate programs

In 3-9 months, gain the skills to break into a new career or take your career to the next level.
undefined Logo
Arizona State University TESOL
Certification preparation•Self-paced
undefined Logo
English Proficiency for Graduate Studies Certificate
Expert feedback•Live sessions
View all Certificates

Health

Get started

Free coursesMost popularGuided Projects under 2 hours

Popular skills

PsychologyMedicineBiologyMedicalNeuroscienceBioinformaticsMental HealthAnatomyFree Courses PsychologyAgricultureView all skills

Degrees

Breakthrough pricing on 100% online degrees designed to fit into your life.
Imperial College London Logo
Imperial College London
Global Master of Public Health
University of Michigan Logo
University of Michigan
Master of Science in Population and Health Sciences
University of Michigan Logo
University of Michigan
Master of Public Health
View all degrees

Certificate programs

In 3-9 months, gain the skills to break into a new career or take your career to the next level.
undefined Logo
Health Informatics MasterTrack® Certificate
Expert feedback•Credit eligible
View all Certificates

Personal Development

Get started

Free coursesMost popularGuided Projects under 2 hours

Popular skills

Communication SkillsSoft SkillsCritical ThinkingPublic SpeakingEmotional IntelligenceFree Courses PsychologyTeachingMindfulnessPositive PsychologyTeaching EnglishView all skills

Certificate programs

In 3-9 months, gain the skills to break into a new career or take your career to the next level.
undefined Logo
CertNexus Certified Ethical Emerging Technologist
Certification preparation•Self-paced
undefined Logo
ICPM Certified Supervisor
Certification preparation•Self-paced
View all Certificates

Physical Science and Engineering

Get started

Free coursesMost popularGuided Projects under 2 hours

Popular skills

MatlabPhysicsCalculusCivil EngineeringElectronicsAutocadGISEmbedded SystemsChemistryArduinoView all skills

Degrees

Breakthrough pricing on 100% online degrees designed to fit into your life.
University of Colorado Boulder Logo
University of Colorado Boulder
Master of Science in Electrical Engineering
View all degrees

Certificate programs

In 3-9 months, gain the skills to break into a new career or take your career to the next level.
undefined Logo
IBM AI Engineering
Self-paced
undefined Logo
Preparing for Google Cloud Certification: Cloud Engineer
Certification preparation•Self-paced
undefined Logo
Industrial Internet of Things MasterTrack® Certificate
Expert feedback•Credit eligible
View all Certificates

Social Sciences

Get started

Free coursesMost popularGuided Projects under 2 hours

Popular skills

LawEconomicsSustainabilityJournalismInternational RelationsTeachingSociologyTeaching EnglishEducationMacroeconomicsView all skills

Degrees

Breakthrough pricing on 100% online degrees designed to fit into your life.
Imperial College London Logo
Imperial College London
Global Master of Public Health
University of Michigan Logo
University of Michigan
Master of Public Health
O.P. Jindal Global University Logo
O.P. Jindal Global University
M.A. in International Relations, Security, and Strategy
View all degrees

Certificate programs

In 3-9 months, gain the skills to break into a new career or take your career to the next level.
undefined Logo
Social Work MasterTrack® Certificate
Expert feedback•Credit eligible
View all Certificates

Arts and Humanities

Get started

Free coursesMost popularGuided Projects under 2 hours

Popular skills

ArtPhotoshopMusicPhotographyCreative WritingDrawingFilmArt HistoryMusic TheoryPhilosophyView all skills

Degrees

Breakthrough pricing on 100% online degrees designed to fit into your life.
University of North Texas Logo
University of North Texas
Bachelor of Applied Arts and Sciences
View all degrees

Certificate programs

In 3-9 months, gain the skills to break into a new career or take your career to the next level.
undefined Logo
Google UX Design
No prerequisites•Self-paced
undefined Logo
UX Design MasterTrack® Certificate
Expert feedback•Credit eligible
View all Certificates

Math and Logic

Get started

Free coursesMost popularGuided Projects under 2 hours

Popular skills

CalculusMathematicsLinear AlgebraAlgebraMathProbabilityMathematics For Machine LearningOptimizationPre CalculusMultivariable CalculusView all skills

Degrees

Breakthrough pricing on 100% online degrees designed to fit into your life.
University of London Logo
University of London
Bachelor of Science in Computer Science
View all degrees
  • Browse
  • Top Courses
  • Profile
  • My Purchases
  • Get 50% Off
  • Settings
  • Updates
  • Accomplishments
  • Help Center
    Coursera
    1. Probability Theory, Statistics and Exploratory Data Analysis
    2. Week 4
    3. Expectation of a function of random variable
    PreviousNext
      • Completed
        Video: LectureIntroduction to the 4th week
        . Duration: 3 minutes3 min
      • Completed
        Video: LectureContinuous random variables. Motivation and Example
        . Duration: 10 minutes10 min
      • Completed
        Video: LectureProbability density function (PDF)
        . Duration: 9 minutes9 min
      • Completed
        Video: LectureCumulative distribution function (CDF)
        . Duration: 13 minutes13 min
      • Completed
        Video: LectureProperties of CDF
        . Duration: 6 minutes6 min
      • Completed
        Quiz: CDF of discrete random variable
        2 questions
      • Completed
        Video: LectureLinking PDF and CDF
        . Duration: 11 minutes11 min
      • Completed
        Video: LectureExamples of probability density functions
        . Duration: 10 minutes10 min
      • Completed
        Quiz: PDF and CDF skill test
        4 questions
      • Completed
        Video: LectureHistogram as approximation to a graph of PDF
        . Duration: 11 minutes11 min
      • Completed
        Video: LectureExpected value of continuous random variable
        . Duration: 9 minutes9 min
      • Completed
        Quiz: Finding expectation with PDF
        1 question
      • Completed
        Video: LectureVariance of continuous random variable. Properties of expected value and variance
        . Duration: 7 minutes7 min
      • Completed
        Quiz: Finding variance with PDF
        1 question
      • Completed
        Video: LectureTransformations of continuous random variables and their PDFs
        . Duration: 11 minutes11 min
      • Completed
        Quiz: Expectation of a function of random variable
        1 question
      • Completed
        Quiz: PDF skill test
        2 questions
      • Completed
        Video: LectureJoint CDF and PDF. Level charts. Marginal PDF
        . Duration: 10 minutes10 min
      • Completed
        Video: LectureIndependence, covariance and correlation of continuous random variables
        . Duration: 9 minutes9 min
      • Completed
        Quiz: Variance of sum of Gaussian random variables
        1 question
      • Completed
        Video: LectureMixed random variables. Example
        . Duration: 11 minutes11 min
      • Completed
        Quiz: Distinguishing random variables
        3 questions
      • Completed
        Video: LectureGenerating and visualizing continuous random variables with Python
        . Duration: 10 minutes10 min
      • Completed
        Video: LectureGenerating correlated random variables with Python
        . Duration: 11 minutes11 min
    QuizQuiz • 2 min2 minutes

    Expectation of a function of random variable

    Activity Completed
    Submit your assignment
    Due DateJun 15, 2:59 AM EDTJune 15, 2:59 AM EDT
    Activity Completed
    Receive grade
    To Pass100% or higher
    Grade
    100%
    We keep your highest score

    Confirm Navigation

    Are you sure you want to leave this page?
      
    ˆ
    Expectation of a function of random variable
    Graded Quiz • 2 min

    Due Jun 15, 2:59 AM EDT

    Check
    Congratulations! You passed!
    To Pass 100% or higher
    Grade
    100%

    Expectation of a function of random variable

    Latest Submission Grade
    100%
    1.
    Question 1

    Find E(πcos⁡πx)\mathbb E(\pi \cos\pi x)E(πcosπx) for XXX uniformly distributed on [0,1]. Enter the value below:

    1 / 1 point
    0
    Check
    Correct